What is -3|x+1|+5>=-1 ?

The solution to -3|x+1|+5>=-1 is -3<= x<= 1

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-3|x+1|+5>=-1

- 3 ∣ x + 1 ∣ + 5 \geq - 1

- 3 \leq x \leq 1

Interval Notation

[- 3, 1]

Solution steps

- 3 ∣ x + 1 ∣ + 5 \geq - 1

Move

5

to the right side

- 3 ∣ x + 1 ∣ \geq - 6

Multiply both sides by

- 1

3 ∣ x + 1 ∣ \leq 6

Divide both sides by

3

∣ x + 1 ∣ \leq 2

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 2 \leq x + 1 \leq 2

x + 1 \geq - 2 and x + 1 \leq 2

x \geq - 3 and x \leq 1

Merge Overlapping Intervals

- 3 \leq x \leq 1

6 = - 3 (4 x + 5) + 9

- 8 x + 44 \geq 60

9 t^{2} - 12 t + 4

\frac{7}{2}

\frac{4 t}{3} + 3 t - 5 = 0